As Ridge pointed out, a fast twist 22cal rifle firing heavy bullets will do things that most 40-50grn shooters would never expect. I've knocked down coyotes past 500yrds with a 223rem in the past 69grn SMK's or Berger 75grn VLD's usually, even just using a 1:9". It's really not that hard to kill game. Fighting the wind with light bullets over long ranges and getting it on target is the larger problem.
A few thoughts on "amping up the .223rem"...
It has been done, in various ways...
.223AI = blown out 223rem case, adds about 2.5grn water capacity, adds 100-150fps more on top of 223rem velocities. I haven't noticed a huge difference, but the guy I bought my reamer from claimed his brass lasted longer as .223AI than it would as .223rem because he could neck-size-only more times and avoid work hardening by full length sizing. I don't anneal myself, just get new brass, and I'm not sure whether annealing 223rem brass would make up the gap against work hardening, but it IS another step. I probably wouldn't AI another 223rem, as I didn't notice nearly the performance gain in the .223 as I have in the 243, but it's an easy change, and does boost performance.
.22-250, 220swift, 223WSSM, then .243win, .25-06, 300win mag... etc etc. Bigger cases, more powder, more potential velocity running a heavier bullet = longer range potential hunting. There's a reason why other cartridges exist, when you max out the capabilities of one case with a given caliber bullet or bullet weight, bump up the capacity, bump up the bullet weight, bump up the caliber...
Putting too much powder, or a different burn rate of powder into a load isn't a free-lunch. When you start pitting your bolt face or sticking cases in your chamber, or worse, separating case heads or blowing your rifle to pieces, then maybe you'll understand why SAAMI has standard pressures for different cartridges, and why reloading manuals have DO NOT EXCEED maximum charge limits. There's also a finite amount of room within a case, so even if you wanted to "just put more powder in there", you can't. .223rem is a small case, so it's no stranger to compressed loads - i.e. powder loads that don't actually fit in the case, so they get compressed when you seat the bullet on top. "Compressed loads" are something not to be taken lightly, and are highly cautioned in those manuals that publish them. Some reloaders I grew up with avoided compressed loads altogether because they claimed it produced erratic velocity spreads (high ES and SD), whether you believe it or not doesn't matter, but when you see someone walking with caution, it's often wise to do so as well until you know what they're cautious of.